Now that the dust has settled somewhat on the rhetorical skirmish between Rand Paul and Chris Christie over NSA data-gathering, it's easier to see the irony of the confrontation.

We witnessed not just the punching and counterpunching of politicians considered likely contenders for the 2016 GOP nomination. It was also a clash between men who each possess a key to winning the White House.

But that's the rub. It takes at least two keys for a Republican to win the White House — one to unlock the Republican electorate of the primaries; the second to woo general-election voters. And the libertarian senator and tough-talking governor seem to be holding different keys.

Paul, the Kentuckian who carries the Tea Party banner in the Senate, would seem to have more appeal to the Republican Party base than does Christie. A recent Pew Research Center survey of Republicans indicates as much.

But Paul has less to offer, at least right now, to the broader universe of general-election voters. What he lacks in that respect however, Christie possesses, as suggested by a recent Public Policy Polling survey.

As governor of decidedly blue New Jersey, Christie is in the center-right tradition of previous Republican occupants of Drumthwacket, the New Jersey governor's official residence. That would very likely make Christie more competitive against a Democratic nominee in battleground states, and could even put New Jersey in play in a general election.

But he would first have to get through the Republican primaries, which could prove a challenge.

So Christie and Paul have related problems. You can see how each could get part of the way down the path to the White House. Less clear is how either goes the distance.

The GOP has faced some version of this challenge — where one politician has stronger appeal to voters inside the party, and another candidate to voters at large — in a number of presidential election cycles.

Recent history might seem to favor Christie, with Republican Party primary voters eventually falling in line behind the candidate seen to have greater crossover appeal to political independents. In 2008, they chose Arizona Sen. John McCain over former Arkansas Gov. Mike Huckabee and former Massachusetts Gov. Mitt Romney. In 2012, it was Romney over former Pennsylvania Sen. Rick Santorum.

It's as though the party hasn't forgotten the 1964 GOP nomination race, when another centrist big-state governor ran for the Republican nomination against a senator who was a right-wing darling with libertarian tendencies.

William Scranton of Pennsylvania, who died in July at age 96, lost that nomination to Sen. Barry Goldwater of Arizona, whom Democratic President Lyndon Johnson crushed in the general election.